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arXiv · 2105.03594

Learning stochastic decision trees

Guy Blanc·Jane Lange·Li-Yang Tan
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Abstract

We give a quasipolynomial-time algorithm for learning stochastic decision trees that is optimally resilient to adversarial noise. Given an $\eta$-corrupted set of uniform random samples labeled by a size-$s$ stochastic decision tree, our algorithm runs in time $n^{O(\log(s/\varepsilon)/\varepsilon^2)}$ and returns a hypothesis with error within an additive $2\eta + \varepsilon$ of the Bayes optimal. An additive $2\eta$ is the information-theoretic minimum. Previously no non-trivial algorithm with a guarantee of $O(\eta) + \varepsilon$ was known, even for weaker noise models. Our algorithm is furthermore proper, returning a hypothesis that is itself a decision tree; previously no such algorithm was known even in the noiseless setting.

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Guy Blanc, Jane Lange, Li-Yang Tan. 2021-05-08. Learning stochastic decision trees. https://arxiv.org/abs/2105.03594

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